spatialHeatmap: Visualizing Spatial Assays in Anatomical Images and Network Graphs

Authors: Jianhai Zhang, Bing Yang, Wolf B. Frommer, Julia Bailey-Serres and Thomas Girke

Package

spatialHeatmap 0.99.0

1 Introduction

1.1 Motivation

The spatialHeatmap package provides functionalities for visualizing cell-, tissue- and organ-specific data of biological assays by coloring the corresponding spatial features defined in anatomical images according to a numeric color key. The color scheme used to represent the assay values can be customized by the user. This core functionality of the package is called a spatial heatmap plot. It is enhanced with nearest neighbor visualization tools for groups of measured items (e.g. gene modules) sharing related abundance profiles, including matrix heatmaps combined with hierarchical clustering dendrograms and network representations. The functionalities of spatialHeatmap can be used either in a command-driven mode from within R or a graphical user interface (GUI) provided by a Shiny App that is also part of this package. While the R-based mode provides flexibility to customize and automate analysis routines, the Shiny App includes a variety of convenience features that will appeal to biologists. Moreover, the Shiny App can be used on both local computers as well as centralized server-based deployments (e.g. cloud-based or custom servers) that can be accessed remotely as a public web service for using spatialHeatmap’s functionalities with community and/or private data. The functionalities of the spatialHeatmap package are illustrated in Figure 1.

Figure 1: Functionality overview
The numeric data can come as a vector, data frame, or SummarizedExperiment (SE). If vector or data frame, the sample and condition identifiers should be in the form of ’sample__condition’, e.g. ’S1__con1’. If data frame or SE, the columns and rows should be sample/conditions and assayed items (gene1, gene2) respectively. In SE, the colData slot is required and contains replicate information, while the rowData slot is optional and contains row item annotation. If the latter is available, the annotation is seen by mousing over a node in the interactive network. In the aSVG image (see aSVG below), spatial features are pre-defined and assigned unique identifiers. In visualization, only aSVG features having identical sample counterparts in data are colored (e.g. S1) in spatial heatmaps. To supplement spatial heatmaps, coexpression analysis is applied on ‘data matrix’ to identify network modules. The gene in spatial heatmaps can be investigated in the gene module it belongs to, where the module is in form of matrix heatmap and network. Lastly, the spatial heatmaps, matrix heatmap, network are all combined as an interactive Shiny app.

As anatomical images the package supports both tissue maps from public repositories and custom images provided by the user. In general any type of image can be used as long as it can be provided in SVG (Scalable Vector Graphics) format, where the corresponding spatial features have been defined (see aSVG below). The numeric values plotted onto a spatial heatmap are usually quantitative measurements from a wide range of profiling technologies, such as microarrays, next generation sequencing (e.g. RNA-Seq and scRNA-Seq), proteomics, metabolomics, or many other small- or large-scale experiments. For convenience, several preprocessing and normalization methods for the most common use cases are included that support raw and/or preprocessed data. Currently, the main application domains of the spatialHeatmap package are numeric data sets and spatially mapped images from biological, agricultural and biomedical areas. Moreover, the package has been designed to also work with many other spatial data types, such a population data plotted onto geographic maps. This high level of flexibility is one of the unique features of spatialHeatmap. Related software tools for biological applications in this field are largely based on pure web applications (Winter et al. 2007; Waese et al. 2017) or local tools (Maag 2018; Muschelli, Sweeney, and Crainiceanu 2014) that typically lack customization functionalities. These restrictions limit users to utilizing pre-existing expression data and/or fixed sets of anatomical image collections. To close this gap for biological use cases, we have developed spatialHeatmap as a generic R/Bioconductor package for plotting quantitative values onto any type of spatially mapped images in a programmable environment and/or in an intuitive to use GUI application.

1.2 Design

The core feature of spatialHeatmap is to map the assay values (e.g. gene expression data) of one or many items (e.g. genes) measured under different conditions in form of numerically graded colors onto the corresponding cell types or tissues represented in a chosen SVG image. In the gene profiling field, this feature supports comparisons of the expression values among multiple genes by plotting their spatial heatmaps next to each other. Similarly, one can display the expression values of a single or multiple genes across multiple conditions in the same plot (Figure 4). This level of flexibility is very efficient for visualizing complicated expression patterns across genes, cell types and conditions. In case of more complex anatomical images composed of overlapping multiple layer tissues, it is important to visually expose the tissue layer of interest in the plots. To address this, several default and customizable layer viewing options are provided. They allow to hide features in the top layers by making them transparent in order to expose features below them. This transparency viewing feature is highlighted below in the mouse example (Figure 6).

To maximize reusability and extensibility, the package organizes large-scale omics assay data along with the associated experimental design information in a SummarizedExperiment object. The latter is one of the core S4 classes within the Bioconductor ecosystem that has been widely adapted by many other software packages dealing with gene-, protein- and metabolite-level profiling data (Morgan et al. 2018). In case of gene expression data, the assays slot of the SummarizedExperiment container is populated with a gene expression matrix, where the rows and columns represent the genes and tissue/conditions, respectively, while the colData slot contains replicate information. The tissues and/or cell type information in the object maps via colData to the corresponding features in the SVG images using unique identifiers for the spatial features (e.g. tissues or cell types). This allows to color the features of interest in an SVG image according to the numeric data stored in a SummarizedExperiment object. For simplicity the numeric data can also be provided as numeric vectors or data frames. This can be useful for testing purposes and/or the usage of simple data sets that may not require the more advanced features of the SummarizedExperiment class, such as measurements with only one or a few data points. Details about how to access the SVG images and properly format the associated expression data are provided in the Supplement section of this vignette.

1.3 Terminology

Spatial heatmaps are images where colors encode numeric values in features of any shape. For plotting spatial heatmaps, Scalable Vector Graphics (SVG) has been chosen as image format since it is a flexible and widely adapted vector graphics format that provides many advantages for computationally embedding numerical and other information in images. SVG is based on XML formatted text describing all components present in images, including lines, shapes and colors. In case of biological images suitable for spatial heatmaps, the shapes often represent anatomical or cell structures. To assign colors to specific features in spatial heatmaps, annotated SVG (aSVG) files are used where the shapes of interest are labeled according to certain conventions so that they can be addressed and colored programmatically. SVGs and aSVGs of anatomical structures can be downloaded from many sources including the repositories described below. Alternatively, users can generate them themselves with vector graphics such as Inkscape. Typically, in aSVGs one or more shapes of a feature of interest, such as the cell shapes of an organ, are grouped together by a common feature identifier. Via these group identifiers one or many feature types can be colored simultaneously in an aSVG according to biological experiments assaying the corresponding feature types with the required spatial resolution. Correct assignment of image features and assay results is assured by using for both the same feature identifiers. The color gradient used to visually represent the numeric assay values is controlled by a color gradient parameter. To visually interpret the meaning of the colors, the corresponding color key is included in the spatial heatmap plots. The formatting details for properly annotating both aSVG images and assay data are provided in the Supplement section of this vignette.

1.4 Data Repositories

If not generated by the user, spatial heatmaps can be generated with data downloaded from various public repositories. This includes gene, protein and metabolic profiling data from databases, such as GEO, BAR and EBI. A particularly useful resource, when working with spatialHeatmap, is the Expression Atlas from EMBL-EBI (Papatheodorou et al. 2018). This online service contains both assay and anatomical images. Its assays data include mRNA and protein profiling experiments for different species, tissues and conditions. The corresponding anatomical image collections are also provided for a wide range of species including animals and plants. In spatialHeatmap several import functions are provided to work with the expression and aSVG repository from the Expression Atlas directly. The aSVG images developed by this project will be deposited in its own repository, where users can contribute their aSVG images that are formatted according to our guidlines. [ThG-Comment: URL and name of your own aSVG repos is missing.] jianhai_comment: a specific repo name will be added later.

1.5 Tutorial Overview

The following sections of this vignette showcase the most important functionalities of the spatialHeatmap package using as initial example a simple to understand toy data set, and then more complex mRNA profiling data from the Expression Atlas. First, spatial heatmap plots are generated for both the toy and mRNA expression data. The latter include gene expression data sets from RNA-Seq and microarray experiments of Human Brain, Mouse Organs, Chicken Organs, and Arabidopsis Shoots. The first three are RNA-Seq data from the Expression Atlas and the last one is a microarray data set from GEO. Second, gene context visualization features are introduced, which facilitate the visualization of gene modules sharing similar expression patterns. This includes the visualization of hierarchical clustering results with traditional matrix heatmaps (Matrix Heatmap) as well co-expression network plots (Network). Third, an overview of the corresponding Shiny App is presented that provides access to the same functionalities as the R functions, but executes them in an interactive environment (Chang et al., n.d.; Chang and Borges Ribeiro 2018). Fourth, more advanced features for plotting customized spatial heatmaps are introduced using the Human Brain data set as an example.

2 Getting Started

2.1 Installation

The spatialHeatmap package should be installed from an R (version \(\ge\) 3.6) session with the BiocManager::install command.

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("spatialHeatmap")

2.2 Load Packages and Documentation

Next, the packages required for running the sample code in this vignette need to be loaded.

library(spatialHeatmap); library(SummarizedExperiment); library(ExpressionAtlas); library(GEOquery)

The following lists the vignette(s) of this package in an HTML browser. Clicking the corresponding name will open this vignette.

browseVignettes('spatialHeatmap')

3 Spatial Heatmaps

3.1 Toy Example

Spatial heatmaps are plotted with the spatial_hm function. To provide a quick and transparent overview how these plots are generated, the following uses a generalized toy example where a vector of random numeric values is generated that are used to color the corresponding features in an aSVG image. The image chosen for this example is an aSVG depicting the human brain. The corresponding image file ‘homo_sapiens.brain.svg’ is included in this package for testing purposes. The path to this image on a user's system, where spatialHeatmap is installed, can be obtained with the system.file function.

# Directory of the aSVG collection.
svg.dir <- system.file("extdata/shinyApp/example", package="spatialHeatmap")
# Path of the target aSVG image.
svg.hum <- system.file("extdata/shinyApp/example", 'homo_sapiens.brain.svg', package="spatialHeatmap")

To identify features of interest in annotated in aSVG images, the return_feature function can be used. The following searches the aSVG images stored in dir for the query terms ‘lobe’ and ‘homo sapiens’ under feature and species, respectively. The identified matches are returned as a data.frame.

feature.df <- return_feature(feature=c('lobe'), species=c('homo sapiens'), remote=FALSE, dir=svg.dir)

## Accessing features... 
## arabidopsis_thaliana.root_cross.svg, gallus_gallus.svg, homo_sapiens.brain.svg, mus_musculus.male.svg, organ_final.svg, root_cross_final.svg, root_roottip_final.svg, shoot_final.svg, shoot_root_final.svg, us_map_final.svg,

feature.df

##          feature             id                    SVG    parent
## 1 occipital lobe UBERON_0002021 homo_sapiens.brain.svg LAYER_EFO
## 2  parietal lobe UBERON_0001872 homo_sapiens.brain.svg LAYER_EFO
## 3  temporal lobe UBERON_0001871 homo_sapiens.brain.svg LAYER_EFO
##   index index1
## 1     9      7
## 2    10      8
## 3    26     24

fnames <- feature.df[, 1]

The following example generates a small numeric toy vector, where the data slot contains four numbers and its name slot is populated with the three feature names obtained from the above aSVG image. In addition, a non-matching entry (here ‘notMapped’) is included for demonstration purposes. Note, the numbers are mapped to features via name matching among the numeric vector and the aSVG, respectively. Accordingly, only numbers and features with matching name counterparts can be colored in the aSVG image. Entries without name matches are indicated by a message printed to the R console, here “notMapped”. This behavior can be turned off with verbose=FALSE in the corresponding function call. In addition, a summary of the numeric assay to feature mappings is stored in the result data.frame returned by the spatial_hm function (see below).

my_vec <- sample(1:100, length(unique(fnames))+1)
names(my_vec) <- c(unique(fnames), 'notMapped')
my_vec

## occipital lobe  parietal lobe  temporal lobe      notMapped 
##             77              8             38             13

Next, the spatial heatmap is plotted with the spatial_hm function (Figure 2). Internally, the numbers in my_vec are translated to colors based on the color key assigned to the col.com argument, and then painted onto the corresponding features in the aSVG, where the path to the image file is defined by svg.path=svg.hum. The remaining arguments used here include: ID for defining the title of the plot; ncol for setting the column-wise layout of the plot excluding the feature legend plot on the right; and height for defining the height of the spatial heatmap relative to its width. In the given example (Figure 2) only three features in my_vec (‘occipital lobe’, ‘parietal lobe’, and ‘temporal lobe’) have matching entries in the corresponding aSVG.

shm.df <- spatial_hm(svg.path=svg.hum, data=my_vec, ID='toy', ncol=1, height=0.7, sub.title.size=20)

## Enrties not mapped: notMapped

Figure 2: Spatial heatmap on toy data
The middle plot is the spatial heatmap and the right is the legend.

The named numeric values in my_vec, that have name matches with the features in the chosen aSVG, are stored in the mapped_feature slot.

# Spatial heatmaps and mapped features are stored in a list.
names(shm.df)

## [1] "spatial_heatmap" "mapped_feature"

# Mapped features
shm.df[['mapped_feature']]

##   rowID     featureSVG value
## 1   toy occipital.lobe    77
## 2   toy  parietal.lobe     8
## 3   toy  temporal.lobe    38

3.2 Human Brain

This subsection introduces how to find cell- and tissue-specific assay data in the Expression Atlas database. After choosing a gene expression experiment, the data is downloaded directly into a user's R session and preprocessed. Subsequently, the processed expression values of genes selected by users are plotted onto a chosen aSVG image. In this case, the query and downloading functionalities of expression data are provided by functionalities of the ExpressionAtlas package (Keays 2019).

The following example searches the Expression Atlas for expression data derived from specific tissues and species of interest, here ‘cerebellum’ and ‘Homo sapiens’, respectively.

all.hum <- searchAtlasExperiments(properties="cerebellum", species="Homo sapiens")

The search result is stored in a DataFrame containing 13 accessions matching the above query. For the following sample code, the accession ‘E-GEOD-67196’ from Prudencio et al. (2015) has been chosen, which corresponds to an RNA-Seq profiling experiment of ‘cerebellum’ and ‘frontal cortex’ brain tissue from patients with amyotrophic lateral sclerosis (ALS). Details about the corresponding record can be returned as follows.

all.hum[2, ]

## DataFrame with 1 row and 4 columns
##      Accession      Species                  Type
##    <character>  <character>           <character>
## 1 E-GEOD-67196 Homo sapiens RNA-seq of coding RNA
##                                                                                                                                   Title
##                                                                                                                             <character>
## 1 Transcription profiling by high throughput sequencing of cerebellum and frontal cortex from patients of amyotrophic lateral sclerosis

The getAtlasData function allows to download the chosen RNA-Seq experiment from the Expression Atlas and import it into a RangedSummarizedExperiment of a user's R session.

Regarding the data type, if the data involves complex samples and conditions (mouse example, chicken example, Arabidopsis example), SummarizedExperiment or RangedSummarizedExperiment is highly recommended. Otherwise, if the data contains simple samples and conditions, it can come as a vector (toy example) or data frame. The function sapatial_hm will distinguish the data types internally. In this example, the default RangedSummarizedExperiment is used. The usage of vector and data frame is detailed in Supplement.

rse.hum <- getAtlasData('E-GEOD-67196')[[1]][[1]]

The design of the downloaded RNA-Seq experiment is described in the colData slot of rse.hum. The following returns only its first five rows and columns.

colData(rse.hum)[1:5, 1:5]

## DataFrame with 5 rows and 5 columns
##            AtlasAssayGroup     organism   individual
##                <character>  <character>  <character>
## SRR1927019              g1 Homo sapiens  individual1
## SRR1927020              g2 Homo sapiens  individual1
## SRR1927021              g1 Homo sapiens  individual2
## SRR1927022              g2 Homo sapiens  individual2
## SRR1927023              g1 Homo sapiens individual34
##             organism_part                       disease
##               <character>                   <character>
## SRR1927019     cerebellum amyotrophic lateral sclerosis
## SRR1927020 frontal cortex amyotrophic lateral sclerosis
## SRR1927021     cerebellum amyotrophic lateral sclerosis
## SRR1927022 frontal cortex amyotrophic lateral sclerosis
## SRR1927023     cerebellum amyotrophic lateral sclerosis

[ThG-Comment 5: please add here the corresponding but unevaluated code to download the aSVG from your repos. Users want to know how this works.]

The following shows how to download the corresponding pre-annotated aSVG image from the EBI SVG repository based on above tissues and species involved. The function return_feature queries the repository with feature and species keywords, i.e. c('frontal cortex', 'cerebellum') and c('homo sapiens', 'brain') respectively. The argument keywords.any is set TRUE by default so that aSVGs containing at least one feature word and one species word are returned. The argument return.all=FALSE means only aSVGs matching the keywords are returned and saved in dir. Otherwise, all aSVGs are returned regardless of the keywords. An empty directory is recommended so as to avoid overwriting existing SVG files with the same names. Here ~/test is used. remote=TRUE means the remote SVG repository is queried. If users want to query a local aSVG collection remote=FALSE should be used, and directory of the local aSVG collection should be provided to dir. match.only is set TRUE so that only matching features are returned. If FALSE, all features in the matching aSVGs are returned.

jianai: The functionality of using EBI online aSVG directly is completed.

# Make an empty directory.
dir.create('~/test')
# Query aSVGs.
feature.df <- return_feature(feature=c('frontal cortex', 'cerebellum'), species=c('homo sapiens', 'brain'), keywords.any=TRUE, return.all=FALSE, dir='~/test', remote=TRUE, match.only=TRUE, desc=FALSE)
# First 8 rows.
feature.df[1:8, ]
# All matching aSVGs.
unique(feature.df$SVG)

As explained in the toy example, the target aSVG image (homo_sapiens.brain.svg) has been included in this package. To meet the requirements for building vignettes in R packages, the following code section uses the packaged instance of the aSVG file (i.e. local aSVG) rather than downloading it. The ontology ids are available in the R package rols (Gatto 2019) or Ontology Lookup Service.

feature.df <- return_feature(feature=c('frontal cortex', 'cerebellum'), species=c('homo sapiens', 'brain'), keywords.any=TRUE, return.all=FALSE, dir=svg.dir, remote=FALSE)

## Accessing features... 
## arabidopsis_thaliana.root_cross.svg, gallus_gallus.svg, homo_sapiens.brain.svg, mus_musculus.male.svg, organ_final.svg, root_cross_final.svg, root_roottip_final.svg, shoot_final.svg, shoot_root_final.svg, us_map_final.svg,

The target tissues frontal cortex and cerebellum in the experiment design are all included in the aSVG, so it can be used for plotting spatial heatmaps. If users want to change the feature identifiers in the aSVG refer to the Supplement for details.

feature.df

##                feature             id                    SVG
## 1 middle frontal gyrus UBERON_0002702 homo_sapiens.brain.svg
## 2     cingulate cortex UBERON_0003027 homo_sapiens.brain.svg
## 3    prefrontal cortex UBERON_0000451 homo_sapiens.brain.svg
## 4       frontal cortex UBERON_0001870 homo_sapiens.brain.svg
## 5      cerebral cortex UBERON_0000956 homo_sapiens.brain.svg
## 6           cerebellum UBERON_0002037 homo_sapiens.brain.svg
##      parent index index1
## 1 LAYER_EFO     8      6
## 2 LAYER_EFO    21     19
## 3 LAYER_EFO    23     21
## 4 LAYER_EFO    24     22
## 5 LAYER_EFO    25     23
## 6 LAYER_EFO    27     25

For downstream plotting purposes it can be desirable to shorten the text in certain columns of colData. This way one can use the source data for including ‘pretty’ sample names in columns and legends of all downstream tables and plots, respectively, in an automated and reproducible manner. To achieve this, the following example imports a ‘targets’ file that can be maintained by the user and is used to replace the text in the colData slot with the shortened version suitable for column titles and legends. This targets file utility is particularly useful for data sets requiring custom annotations.

hum.tar <- system.file('extdata/shinyApp/example/target_human.txt', package='spatialHeatmap')
target.hum <- read.table(hum.tar, header=TRUE, row.names=1, sep='\t')

Use the tagets file to replace the data frame in colData slot.

jianhai_comment: DataFrame should be used otherewise errors arise, so I isolated this code chunk to emphasise it.

colData(rse.hum) <- DataFrame(target.hum)

A slice of the simplified colData object is shown below, where the disease column contains now shorter labels than in the original data set. Additional details for generating and using targets files in spatialHeatmap are provided in the Supplement of this vignette.

colData(rse.hum)[c(1:3, 41:42), 4:5]

## DataFrame with 5 rows and 2 columns
##             organism_part     disease
##               <character> <character>
## SRR1927019     cerebellum         ALS
## SRR1927020 frontal cortex         ALS
## SRR1927021     cerebellum         ALS
## SRR1927059     cerebellum      normal
## SRR1927060 frontal cortex      normal

The actual expression data of the downloaded RNA-Seq experiment is stored in the assay slot of rse.hum. Since it contains raw count data, it is often beneficial to apply prior to plotting spatial heatmaps basic preprocessing routines. The following shows how to normalize the count data, aggregate replicates and then remove genes with unreliable expression responses.

[ThG-Comment 4: can you please substantially improve the below text in the following preprocessing code step as well as the help files of the corresponding functions. I am not able to follow why and how certain parts are done. For instance, why is ratio used as a normalization method? The final result also does not seem to be log ratios. You need to better describe what you are doing here. Asking readers to look through your code is not appropriate for a package.] Added

The raw-count normalizing function is norm_data. It builds on calcNormFactors (CNF) from edgeR (McCarthy et al. 2012), and estimateSizeFactors (EST), varianceStabilizingTransformation (VST), rlog from DESeq2 (Love, Huber, and Anders 2014). The argument norm.fun specifies one of the four internal normalizing functions: CNF, EST, VST, rlog. If none, no normalization is applied. The arguments of each internal normalizing function are provided through parameter.list, which is a named list. For example, norm.fun='ESF' and parameter.list=list(type='ratio') is equivalent to estimateSizeFactors(object, type='ratio').

If paramter.list=NULL, the default arguments are applied for the normalizing function provided to norm.fun. See the help file of norm_data for details by running ?norm_data in R console. In this example, ESF is chose for faster speed.

# Normalise.
se.nor.hum <- norm_data(data=rse.hum, norm.fun='ESF', data.trans='log2')

## Normalising: ESF 
##    type 
## "ratio"

The replicates used for aggregation is generated by concatenating the ‘sample’ and ‘contition’ column in colData slot with double underscore (__). The former is specified by sam.factor and the latter by con.factor. For example, in the following, organism_part is sample and disease is condition. Thus cerebellum__ALS, frontal_cortex__ALS, cerebellum__normal, frontal_cortex__normal are generated as ’sample__condition’ replicates and aggregated.

# Aggregate replicates.
se.aggr.hum <- aggr_rep(data=se.nor.hum, sam.factor='organism_part', con.factor='disease', aggr='mean')
assay(se.aggr.hum)[1:3, ]

##                 cerebellum__ALS frontal.cortex__ALS
## ENSG00000000003        7.024054            7.091484
## ENSG00000000005        0.000000            1.540214
## ENSG00000000419        7.866582            8.002549
##                 cerebellum__normal frontal.cortex__normal
## ENSG00000000003           6.406157               7.004446
## ENSG00000000005           0.000000               1.403110
## ENSG00000000419           8.073264               7.955709

The filtering removes unreliable expression measures. Specifically, the following example eliminates genes with expression values larger than 5 (log2 unit) in at least 1% of all samples (pOA=c(0.01, 5)), and with coefficient of variance (CV) between 0.30 and 100 (CV=c(0.30, 100)) are retained.

# Filter genes with low variance and low counts.
se.fil.hum <- filter_data(data=se.aggr.hum, sam.factor='organism_part', con.factor='disease', pOA=c(0.01, 5), CV=c(0.3, 100), dir=NULL)

To inspect the results, the following returns three selected rows of the fully preprocessed data matrix (Table 1).

assay(se.fil.hum)[733:735, ]

Table 1: A slice of fully preprocessed data matrix.

	cerebellum__ALS	frontal.cortex__ALS	cerebellum__normal	frontal.cortex__normal
ENSG00000268433	5.324064	0.3419665	3.478074	0.1340332
ENSG00000268555	5.954572	2.6148548	4.934974	2.0351776
ENSG00000269113	7.544417	1.7425299	6.808402	0.9694065

Next, the preprocessed expression values of gene ENSG00000268433 are plotted onto the corresponding features of the aSVG image depicting the human brain.

shm.df <- spatial_hm(svg.path=svg.hum, data=se.fil.hum, ID=c('ENSG00000268433'), height=0.6, legend.r=1.3)

Figure 3: Spatial heatmaps of human brain
Cerebellum and frontal cortex are colored, since they are the only 2 identical tissues between the aSVG image and the data.

The spatial heatmaps and mapped features are stored in a list and assigned to an object shm.df.

names(shm.df)

## [1] "spatial_heatmap" "mapped_feature"

# Mapped features
shm.df[['mapped_feature']]

##             rowID     featureSVG condition     value
## 1 ENSG00000268433     cerebellum       ALS 5.3240638
## 2 ENSG00000268433 frontal.cortex       ALS 0.3419665
## 3 ENSG00000268433     cerebellum    normal 3.4780744
## 4 ENSG00000268433 frontal.cortex    normal 0.1340332

In this example, the expression profile of gene ENSG00000268433 in frontal cortex and cerebellum is plotted under ALS and normal conditions (Figure 3) with the legend plot on the right. For example, in Table 1 its expression value in cerebellum under ALS is 5.324064. After mapping, this tissue is colored blue corresponding to 5.324064 in the color scale. By contrast, this gene's expression profile is dark yellow in the same tissue under normal condition. On the other hand, the expression profile (purple) in frontal cortex is similar across ALS and normal. Therefore, it is intuitive that this gene's higher activity in cerebellum is potentially associated with ALS and could contribute to hypothesis generation.

Note that only frontal cortex and cerebellum are colored while others are blank in the spatial heatmaps, since they are the only 2 aSVG features having identical tissue counterpars in the data. And the legend plot only shows these 2 tissues, because sam.legend=identical limits the legend to matching tissues between the data and aSVG. If sam.legend=all, all tissues are shown and legend plot would overlap with spatial heatmaps. Except for identical and all, sam.legend also accepts a vector of specific tissues for display.

[ThG-Comment 6: I suggest to include here a table where you summarize all arguments relevant for controlling the output of spatial_hm function. This will make it much easier for the user to look up relevant arguments and how to use them.] Added

In cases of multiple input genes, and/or multiple conditions, the subplots of spatial heatmaps might get squeezed. To achieve optimal appearance, the main function spatial_hm is designed to be as flexible as possible to avoid such issues. The flexibility is carried out by the arguments listed in Table 2.

Table 2: Description of arguments in “spatial_hm”.

argument	description
svg.path	Path of aSVG
data	Input data of SummarizedExperiment (SE), data frame, or vector
sam.factor	Applies to SE. Column name of sample replicates in colData slot. Default is NULL
con.factor	Applies to SE. Column name of condition replicates in colData slot. Default is NULL
ID	A character vector of row features for plotting spatial heatmaps
col.com	A character vector of colour components for building colour scale. Default is c(‘purple’, ‘yellow’, ‘blue’)
col.bar	‘selected’ or ‘all’, the former means use values of ID to build the colour scale while the latter use all values in data. Default is ‘selected’.
bar.width	A numeric of colour bar width. Default is 0.7
data.trans	‘log2’, ‘exp2’, or NULL, ‘log2’ transforms data to log2 scale for plotting while ‘exp2’ to 2-base exponent. Default is NULL, no transformation.
tis.trans	A vector of aSVG features to be transparent. Default is NULL.
width, height	Two numerics of width and height of spatial heatmap plots repsectively. Default is 1, 1.
legend.r	The ratio aspect (width to height) of legend plot. Default is 1.
sub.title.size	The title size of each spatial heatmap subplot. Default is 11.
lay.shm	‘gen’ or ‘con’, applies to multiple genes or conditions respectively. ‘gen’ means spatial heatmaps are organised by genes while ‘con’ organised by conditions.Default is ‘gen’
ncol	The column number of spatial heatmaps, not including legend plot. Default is 2.
sam.legend	‘identical’, ‘all’, or a vector of samples/features in aSVG to show in legend plot. ‘identical’ only shows matching features while ‘all’ shows all features.
legend.ncol, legend.nrow	Two numbers of columns and rows of legend keys respectively. Default is NULL, NULL, since they are automatically set.
legend.position	the position of legend keys (‘none’, ‘left’, ‘right’,‘bottom’, ‘top’), or two-element numeric vector. Default is ‘bottom’.
legend.direction	Layout of keys in legends (‘horizontal’ or ‘vertical’). Default is NULL, since it is automatically set.
legend.key.size, legend.label.size	The size of legend keys and labels respectively. Default is 0.5 and 8 respectively.
line.size, line.color	The size and colour of all plogyon outlines respectively. Default is 0.2 and ‘grey70’ respectively.
verbose	TRUE or FALSE. Default is TRUE and the aSVG features not mapped are printed to R console.

[ThG-Comment 7: The paragraphs below have been moved here for now. There is a lot of duplication in this text that needs to be deleted (or hidden via comment tags) and/or merged into other sections where appropriate. Some of the text is certainly important but it often should be used to explain code sections rather than keeping it separate from the code. For instance the first paragraph below should go to a section where you show how to generate multiple target gene plots rather then just describing it in stand-alone text, especially since a summary of this particular example has been given in the intro section already.]

Moved

If mutiple target genes are input, a set of spatial heatmaps for each gene are plotted sequentially and organised on the same page. The lay.shm parameter specifies display these spatial heatmaps by genes or by conditions. This feature makes it flexible for users to compare expression profiles of the same gene across conditions or different genes across the same condition, and is particularly useful when compare gene families. For instance, Figure 4 is the spatial heatmaps of gene ENSG00000268433 and ENSG00000006047, which are organised by condition (horizontal view).

spatial_hm(svg.path=svg.hum, data=se.fil.hum, ID=c('ENSG00000268433', 'ENSG00000006047'), lay.shm='con', width=1, height=1, legend.r=1.5)

Figure 4: Spatial heatmaps of two genes
The subplots are organised by “condition” through lay.shm argument.

3.3 Mouse Organ

This example is based on a mouse data from an RNA-seq study aiming at assessing tissue-specific transcriptome variation across mammals (Merkin et al. 2012), which is from EBI Expression Atlas.

The following process is similar to the Human Brain example, so explanation of code chunks is simplified to avoid lengthy text.

Search Expression Atlas for expression data derived from ‘hear’ and ‘Mus musculus’.

all.mus <- searchAtlasExperiments(properties="heart", species="Mus musculus")

Among the results, select ‘E-MTAB-2801’.

all.mus[7, ]

## DataFrame with 1 row and 4 columns
##     Accession      Species                  Type
##   <character>  <character>           <character>
## 1 E-MTAB-2801 Mus musculus RNA-seq of coding RNA
##                                           Title
##                                     <character>
## 1 Strand-specific RNA-seq of nine mouse tissues

rse.mus <- getAtlasData('E-MTAB-2801')[[1]][[1]]

A slice of the experiment design, which is stored in colData slot.

colData(rse.mus)[1:3, ]

## DataFrame with 3 rows and 4 columns
##           AtlasAssayGroup     organism organism_part      strain
##               <character>  <character>   <character> <character>
## SRR594393              g7 Mus musculus         brain      DBA/2J
## SRR594394             g21 Mus musculus         colon      DBA/2J
## SRR594395             g13 Mus musculus         heart      DBA/2J

Download aSVGs from remote EBI repository directly based on tissues and species involved. An empty directory ~/test is suggested to save the downloaded files so as to avoid overwriting existing files.

# Make an empty directory "~/test" if not exist.
if (!dir.exists('~/test')) dir.create('~/test')
# Query aSVGs.
feature.df <- return_feature(feature=c('heart', 'kidney'), species=c('Mus musculus'), keywords.any=TRUE, return.all=FALSE, dir='~/test', remote=TRUE, match.only=FALSE)

As explained in the toy example, the target aSVG file has been included in this package. To meet the requirements for building vignettes in R packages, the following code section uses the packaged instance of the aSVG files (remote=FALSE) rather than downloading it. To explain how to select a certain aSVG among the returned resutls, species is set NULL on purpose so that all aSVGs marching the feature keywords are returned.

feature.df <- return_feature(feature=c('heart', 'kidney'), species=NULL, keywords.any=TRUE, return.all=FALSE, dir=svg.dir, remote=FALSE, match.only=FALSE) 

## Accessing features... 
## arabidopsis_thaliana.root_cross.svg, gallus_gallus.svg, homo_sapiens.brain.svg, mus_musculus.male.svg, organ_final.svg, root_cross_final.svg, root_roottip_final.svg, shoot_final.svg, shoot_root_final.svg, us_map_final.svg,

All aSVG files matching the query.

unique(feature.df$SVG)

## [1] "gallus_gallus.svg"     "mus_musculus.male.svg"

Select mus_musculus.male.svg as the target aSVG. A slice of the feature data frame and all the aSVG features are shown.

feature.df <- subset(feature.df, SVG=='mus_musculus.male.svg')
# A slice of the feature data frame.
feature.df[1:3, ]

##     feature             id                   SVG        parent
## 10   kidney UBERON_0002113 mus_musculus.male.svg     LAYER_EFO
## 11    heart UBERON_0000948 mus_musculus.male.svg     LAYER_EFO
## 12 path4204       path4204 mus_musculus.male.svg LAYER_OUTLINE
##    index index1
## 10    14     12
## 11    51     49
## 12     1      1

# All features in the aSVG.
unique(feature.df[, 1])

##  [1] "kidney"                    "heart"                    
##  [3] "path4204"                  "aorta"                    
##  [5] "circulatory system"        "blood vessel"             
##  [7] "brown adipose tissue"      "white adipose tissue"     
##  [9] "skin"                      "stomach"                  
## [11] "duodenum"                  "pancreas"                 
## [13] "spleen"                    "adrenal gland"            
## [15] "colon"                     "small intestine"          
## [17] "caecum"                    "jejunum"                  
## [19] "ileum"                     "esophagus"                
## [21] "gall bladder"              "parotid gland"            
## [23] "submandibular gland"       "lymph node"               
## [25] "parathyroid gland"         "tongue"                   
## [27] "Peyer’s patch"             "prostate gland"           
## [29] "vas deferens"              "epididymis"               
## [31] "testis"                    "seminal vesicle"          
## [33] "penis"                     "urinary bladder"          
## [35] "thymus"                    "femur"                    
## [37] "bone marrow"               "cartilage"                
## [39] "quadriceps femoris"        "spinal cord"              
## [41] "lung"                      "diaphragm"                
## [43] "peripheral nervous system" "trachea"                  
## [45] "hindlimb"                  "trigeminal nerve"         
## [47] "eye"                       "sciatic nerve"            
## [49] "intestinal mucosa"         "liver"                    
## [51] "brain"                     "skeletal muscle"

Get the target aSVG path.

svg.mus <- system.file("extdata/shinyApp/example", "mus_musculus.male.svg", package="spatialHeatmap")

Make a targets file based on the experiment design and features of interest in the aSVG file. It is included in this package and part is shown below.

mus.tar <- system.file('extdata/shinyApp/example/target_mouse.txt', package='spatialHeatmap')
target.mus <- read.table(mus.tar, header=TRUE, row.names=1, sep='\t')
target.mus[1:3, ]

##           AtlasAssayGroup     organism organism_part strain
## SRR594393              g7 Mus musculus         brain DBA.2J
## SRR594394             g21 Mus musculus         colon DBA.2J
## SRR594395             g13 Mus musculus         heart DBA.2J

# Tissues in the experiment. 
unique(target.mus[, 3])

## [1] "brain"           "colon"           "heart"          
## [4] "kidney"          "liver"           "lung"           
## [7] "skeletal muscle" "spleen"          "testis"

Use the targets file to replace the data frame in colData slot.

colData(rse.mus) <- DataFrame(target.mus)

Pre-process the raw count matrix: normalise, aggregate, filter. Genes with expression values larger than 5 (log2 unit) in at least 1% of all samples (pOA=c(0.01, 5)), and with coefficient of variance (CV) between 0.60 and 100 (CV=c(0.6, 100)) are retained.

# Normalise.
se.nor.mus <- norm_data(data=rse.mus, norm.fun='ESF', data.trans='log2')

## Normalising: ESF 
##    type 
## "ratio"

# Aggregate replicates.
se.aggr.mus <- aggr_rep(data=se.nor.mus, sam.factor='organism_part', con.factor='strain', aggr='mean')
# Filter genes with low variance and low counts.
se.fil.mus <- filter_data(data=se.aggr.mus, sam.factor='organism_part', con.factor='strain', pOA=c(0.01, 5), CV=c(0.6, 100), dir=NULL)

Plot spatial heatmaps.

spatial_hm(svg.path=svg.mus, data=se.fil.mus, ID=c('ENSMUSG00000000263'), height=0.5, legend.r=1.1, sub.title.size=9, ncol=3, tis.trans=c('skeletal muscle'), legend.nrow=4, line.size=0.2, line.color='grey70')

Figure 5: Mouse organ spatial heatmap
This is a multiple-layer image and skeletal muscle is set transparent to expose lung and heart.

The spatial heatmap of gene ENSMUSG00000000263 is plotted in 8 tissues across 3 strains. It is manifest that only brain exhibits obvious difference across the 3 strains with DBA.2J, C57BL.6, and CD1 being highest, medium, and lowest respectively. In contrast, all the other 8 tissues display similar profile across strains. Thus this gene is potentially strain-specific. Moreover, the expression levels of all the other 8 tissues are all lower than brain.

This is a typical example to demonstrate the usage of tis.trans parameter, since this mouse organ image includes tissues in multiple layers and skelectal muscle covers lung and heart. In Figure 5, skelectal muscle is set transparent through tis.trans=c('skeletal muscle') so that lung and heart are exposed. By contrast, in Figure 6 tis.trans=NULL exposes skeletal muscle and lung and heart are covered.

Moreover, presence of too many tissues might affect the visual effects due to the messy polygon outlines. The line.size and line.color parameters are used to adjust the thickness and color of polygon outlines respectively and thus enhance the visualisation. In Figure 2, the default values of the 2 arguments are used.

spatial_hm(svg.path=svg.mus, data=se.fil.mus, ID=c('ENSMUSG00000000263'), height=0.5, legend.r=1.1, sub.title.size=9, ncol=3, tis.trans=NULL, legend.ncol=2, line.size=0.2, line.color='grey70')

Figure 6: Mouse organ spatial heatmap
This is a multiple-layer image and skeletal muscle convers lung and heart.

3.4 Chicken Organ

In this example, the data come from developments of 7 chicken organs under 9 time points (Cardoso-Moreira et al. 2019), which is an RNA-seq analysis and accessed from EBI Expression Atlas.

The following process is similar to the Human Brain example, so explanation of code chunks is simplified to avoid lengthy text.

Search Expression Atlas for expression data derived from ‘heart’ and ‘gallus’.

all.chk <- searchAtlasExperiments(properties="heart", species="gallus")

Among the results, select ‘E-MTAB-6769’.

all.chk[3, ]

## DataFrame with 1 row and 4 columns
##     Accession       Species                  Type
##   <character>   <character>           <character>
## 1 E-MTAB-6769 Gallus gallus RNA-seq of coding RNA
##                                                                  Title
##                                                            <character>
## 1 Chicken RNA-seq time-series of the development of seven major organs

rse.chk <- getAtlasData('E-MTAB-6769')[[1]][[1]]

A slice of the experiment design, which is stored in colData slot.

colData(rse.chk)[1:3, ]

## DataFrame with 3 rows and 8 columns
##            AtlasAssayGroup      organism         strain
##                <character>   <character>    <character>
## ERR2576379              g1 Gallus gallus Red Junglefowl
## ERR2576380              g1 Gallus gallus Red Junglefowl
## ERR2576381              g2 Gallus gallus Red Junglefowl
##                      genotype developmental_stage         age
##                   <character>         <character> <character>
## ERR2576379 wild type genotype              embryo      10 day
## ERR2576380 wild type genotype              embryo      10 day
## ERR2576381 wild type genotype              embryo      10 day
##                    sex organism_part
##            <character>   <character>
## ERR2576379      female         brain
## ERR2576380      female         brain
## ERR2576381      female    cerebellum

Download aSVGs from EBI repository based on the tissues and species involved. An empty directory ~/test is suggested to save the downloaded files so as to avoid overwriting existing files.

# Make an empty directory "~/test" if not exist.
if (!dir.exists('~/test')) dir.create('~/test')
# Query aSVGs.
feature.df <- return_feature(feature=c('heart', 'kidney'), species=c('gallus'), keywords.any=TRUE, return.all=FALSE, dir='~/test', remote=TRUE, match.only=FALSE)

As explained in the toy example, the target aSVG image has been included in this package, and will be used for plotting spatial heatmaps.

feature.df <- return_feature(feature=c('heart', 'kidney'), species=c('gallus'), keywords.any=TRUE, return.all=FALSE, dir=svg.dir, remote=FALSE, match.only=FALSE)

## Accessing features... 
## arabidopsis_thaliana.root_cross.svg, gallus_gallus.svg, homo_sapiens.brain.svg, mus_musculus.male.svg, organ_final.svg, root_cross_final.svg, root_roottip_final.svg, shoot_final.svg, shoot_root_final.svg, us_map_final.svg,

feature.df

##                 feature              id               SVG
## 1                 heart  UBERON_0000948 gallus_gallus.svg
## 2                kidney  UBERON_0002113 gallus_gallus.svg
## 3       chicken_outline chicken_outline gallus_gallus.svg
## 4                 brain  UBERON_0000955 gallus_gallus.svg
## 5                 liver  UBERON_0002107 gallus_gallus.svg
## 6 skeletal muscle organ  UBERON_0014892 gallus_gallus.svg
## 7                 colon  UBERON_0001155 gallus_gallus.svg
## 8                spleen  UBERON_0002106 gallus_gallus.svg
## 9                  lung  UBERON_0002048 gallus_gallus.svg
##          parent index index1
## 1     LAYER_EFO     4      2
## 2     LAYER_EFO     5      3
## 3 LAYER_OUTLINE     1      1
## 4     LAYER_EFO     3      1
## 5     LAYER_EFO     6      4
## 6     LAYER_EFO     7      5
## 7     LAYER_EFO     8      6
## 8     LAYER_EFO     9      7
## 9     LAYER_EFO    10      8

Get the target aSVG path.

svg.chk <- system.file("extdata/shinyApp/example", "gallus_gallus.svg", package="spatialHeatmap")

Make a targets file based on the experiment design and features of interest in the aSVG. It is included in this package and part is shown below.

chk.tar <- system.file('extdata/shinyApp/example/target_chicken.txt', package='spatialHeatmap')
target.chk <- read.table(chk.tar, header=TRUE, row.names=1, sep='\t')
target.chk[1:3, ]

##            AtlasAssayGroup      organism         strain
## ERR2576379              g1 Gallus gallus Red Junglefowl
## ERR2576380              g1 Gallus gallus Red Junglefowl
## ERR2576381              g2 Gallus gallus Red Junglefowl
##                      genotype developmental_stage   age    sex
## ERR2576379 wild type genotype              embryo day10 female
## ERR2576380 wild type genotype              embryo day10 female
## ERR2576381 wild type genotype              embryo day10 female
##            organism_part
## ERR2576379         brain
## ERR2576380         brain
## ERR2576381    cerebellum

Use the targets file to replace the data frame in colData slot.

colData(rse.chk) <- DataFrame(target.chk)

All samples used for plotting spatial heatmaps.

unique(colData(rse.chk)[, 'organism_part'])

## [1] "brain"      "cerebellum" "heart"      "kidney"    
## [5] "ovary"      "testis"     "liver"

All conditions used for plotting spatial heatmaps.

unique(colData(rse.chk)[, 'age'])

## [1] "day10"  "day12"  "day14"  "day17"  "day0"   "day155"
## [7] "day35"  "day7"   "day70"

Pro-process data matrix: normalize, aggregate, filter. Genes with expression values larger than 5 (log2 unit) in at least 1% of all samples (pOA=c(0.01, 5)), and with coefficient of variance (CV) between 0.6 and 100 (CV=c(0.6, 100)) are retained.

# Normalise.
se.nor.chk <- norm_data(data=rse.chk, norm.fun='ESF', data.trans='log2')

## Normalising: ESF 
##    type 
## "ratio"

# Aggregate replicates. 
se.aggr.chk <- aggr_rep(data=se.nor.chk, sam.factor='organism_part', con.factor='age', aggr='mean')
# Filter genes with low variance and low counts.
se.fil.chk <- filter_data(data=se.aggr.chk, sam.factor='organism_part', con.factor='age', pOA=c(0.01, 5), CV=c(0.6, 100), dir=NULL)

Plot spatial heatmaps.

spatial_hm(svg.path=svg.chk, data=se.fil.chk, ID='ENSGALG00000006346', legend.r=1.5, sub.title.size=9, ncol=3, legend.nrow=2)

## Enrties not mapped: cerebellum, ovary, testis

Figure 7: Example of plotting chicken organ spatial heatmaps
Liver in day10 is not plotted since this tissue in day10 in not available in the data matrix.

The spatial heatmap of gene ENSGALG00000006346 is plotted. It is intuitive that the profiles of liver, heart, and kidney are all higher in day17 than other days. Therefore, the important role of this gene in day10 is worth futher exploration. In day10 liver is blank, because in the expression matrix liver data is not availble for day10. This reflects the plotting algorithm that only matching samples between the data and SVG image are plotted.

In this example, the usage of argument ncol is exhibited on how to achieve optimal layout. There are 9 time conditions, so ncol=3 is set to make make full use of the space.

3.5 Arabidopsis Shoot

GEO is a another well-known public repository of array- and sequence-based data. To demonstrate the use of spatialHeatmap on this resource, the dataset GSE14502 is plotted on a shoot aSVG image. It a microarray data from a study of translatome variation of Arabidopsis thaliana (Arabidopsis) shoot and root tissues under control and hypoxia conditions (Mustroph et al. 2009), and is downloaded through GEOquery (S. Davis and Meltzer 2007).

Access the GEO dataset GSE14502 and convert it to SummarizedExperiment.

gset <- getGEO("GSE14502", GSEMatrix=TRUE, getGPL=TRUE)[[1]]
se.sh <- as(gset, "SummarizedExperiment")

Use gene symbols to replace probes.

rownames(se.sh) <- make.names(rowData(se.sh)[, 'Gene.Symbol'])

A slice of the experiment design, which is stored in colData slot. The samples and conditions are included in the title column. In samples, promoter pGL2, pCO2, pSCR, pWOL labels root atrichoblast epidermis, root cortex meristematic zone, root endodermis, root vasculature respectively, and p35S labels root_total and shoot_total. There are 2 conditions: control and hypoxia.

colData(se.sh)[60:63, 1:4]

## DataFrame with 4 rows and 4 columns
##                              title geo_accession
##                        <character>   <character>
## GSM362227  shoot_hypoxia_pGL2_rep1     GSM362227
## GSM362228  shoot_hypoxia_pGL2_rep2     GSM362228
## GSM362229 shoot_control_pRBCS_rep1     GSM362229
## GSM362230 shoot_control_pRBCS_rep2     GSM362230
##                          status submission_date
##                     <character>     <character>
## GSM362227 Public on Oct 12 2009     Jan 21 2009
## GSM362228 Public on Oct 12 2009     Jan 21 2009
## GSM362229 Public on Oct 12 2009     Jan 21 2009
## GSM362230 Public on Oct 12 2009     Jan 21 2009

In this example, the aSVG image of Arabidopsis is made from Mustroph et al. (2009). Similarly, it is included in this packaged and thus can be queried locally. The instructions on how to make custom aSVG images are provided in the SVG tutorial.

Query the packaged aSVG files.

feature.df <- return_feature(feature=c('pGL2', 'pRBCS'), species=c('shoot'), keywords.any=TRUE, return.all=FALSE, dir=svg.dir, remote=FALSE, match.only=FALSE)

## Accessing features... 
## arabidopsis_thaliana.root_cross.svg, gallus_gallus.svg, homo_sapiens.brain.svg, mus_musculus.male.svg, organ_final.svg, root_cross_final.svg, root_roottip_final.svg, shoot_final.svg, shoot_root_final.svg, us_map_final.svg,

All matching aSVGs.

unique(feature.df$SVG)

## [1] "shoot_final.svg"      "shoot_root_final.svg"

Select ‘shoot_final.svg’ for plotting spaital heatmaps.

feature.df <- subset(feature.df, SVG=='shoot_final.svg')
# A slice of the feature data frame.
feature.df[1:3, ]

##       feature          id             SVG    parent index index1
## 1  shoot_pGL2  shoot_pGL2 shoot_final.svg container     2      2
## 2 shoot_pRBCS shoot_pRBCS shoot_final.svg container     3      3
## 3        g258        g258 shoot_final.svg container     1      1

Get path of ‘shoot_final.svg’.

svg.sh <- system.file("extdata/shinyApp/example", "shoot_final.svg", package="spatialHeatmap")

Make a targets file based on the title column in experiment design and features of interest in the aSVG. It is included in this package and part is shown below.

sh.tar <- system.file('extdata/shinyApp/example/target_arab.txt', package='spatialHeatmap')
target.sh <- read.table(sh.tar, header=TRUE, row.names=1, sep='\t')
target.sh[60:63, ]

##                           col.name     samples conditions
## shoot_hypoxia_pGL2_rep1  GSM362227  shoot_pGL2    hypoxia
## shoot_hypoxia_pGL2_rep2  GSM362228  shoot_pGL2    hypoxia
## shoot_control_pRBCS_rep1 GSM362229 shoot_pRBCS    control
## shoot_control_pRBCS_rep2 GSM362230 shoot_pRBCS    control

All samples in targets file.

unique(target.sh[, 'samples'])

##  [1] "root_total"      "root_p35S"       "root_pSCR"      
##  [4] "root_pSHR"       "root_pWOL"       "root_pGL2"      
##  [7] "root_pSUC2"      "root_pSultr2.2"  "root_pCO2"      
## [10] "root_pPEP"       "root_pRPL11C"    "shoot_total"    
## [13] "shoot_p35S"      "shoot_pGL2"      "shoot_pRBCS"    
## [16] "shoot_pSUC2"     "shoot_pSultr2.2" "shoot_pCER5"    
## [19] "shoot_pKAT1"

All conditions in targets file.

unique(target.sh[, 'conditions'])

## [1] "control" "hypoxia"

Use the targets file to replace the data frame in colData slot.

colData(se.sh) <- DataFrame(target.sh)

The dataset GSE14502 is already normalised by RMA (Gautier et al. 2004), so the pro-processing only includes aggregation and filtering. Genes with expression values larger than 6 (log2 unit) in at least 3% of all samples (pOA=c(0.03, 6)), and with coefficient of variance (CV) between 0.30 and 100 (CV=c(0.30, 100)) are retained.

# Aggregate replicates. 
se.aggr.sh <- aggr_rep(data=se.sh, sam.factor='samples', con.factor='conditions', aggr='mean')
# Filter genes with low variance and low intensity.
se.fil.arab <- filter_data(data=se.aggr.sh, sam.factor='samples', con.factor='conditions', pOA=c(0.03, 6), CV=c(0.30, 100), dir=NULL)

Plot spatial heatmaps.

spatial_hm(svg.path=svg.sh, data=se.fil.arab, ID=c("HRE2"), height=0.6, legend.nrow=3, legend.r=1.3, legend.key.size=0.3)

## Enrties not mapped: root_total, root_p35S, root_pSCR, root_pSHR, root_pWOL, root_pGL2, root_pSUC2, root_pSultr2.2, root_pCO2, root_pPEP, root_pRPL11C, shoot_total, shoot_p35S

Figure 8: Spatial heatmaps of Arabidopsis shoot
Pre-defined tissue regions are colored by the expression profile of the target gene. The promoter pGL2, pRBCS, pCER5, pSultr2.2, pSUC2, pKAT1 label shoot trichomes, shoot photosynthetic cell, cotyledon and leaf epidermis, shootbundle sheath, shoot phloem companion cells, Cotyledon and leaf guard cells, respectively.

Figure 8 is the spatial heatmap of gene HRE2 under control and hypoxia. It is clear that this gene's exression profiles under control are lower than hypoxia across all the 5 tissues (pGL2, pRBCS, pCER5, pSUC2, pKAT1). Therefore, it can be hypothesised that hypoxia induces over-expression of HRE2 across the 5 tissues and thus HRE2 might be an important factor for Arabidopsis shoot to cope with hypoxia stress. The tissue pSultr2.2 is blank under hypoxia due to unavailability of its data under hypoxia in the data matrix.

jianhai_comment: From here to Shiny App section, slight changes are made.

4 Matrix Heatmaps

The Matrix Heatmap is designed to supplement the core feature of spatial heatmap. It displays the target gene in the context of corresponding gene network module, so there is a process of gene modules identification.

Adjacency Matrix and Module Identification

The modules are identified by adj_mod. It first computes an adjacency matrix on the gene expression matrix then hierarchically clusters the adjacency matrix by using WGCNA (Langfelder and Horvath 2008) and flashClust (Langfelder and Horvath 2012). The clutersing includes 4 alternative sensitivity levels (ds=0, 1, 2, or 3). From 3 to 0, the sensitivity decreases and results in less modules with larger sizes. Since the interactive network functionality performs better on smaller modules, only ds of 3 and 2 are used. There is another parameter type for module identification: signed and unsinged. The former means both positive and negative adjacency between genes are used while the latter takes the absolute values of negative adjacency.

The function adj_mod returns a list containing an adjacency matrix and a data frame of module assignment. It is domenstrated on the Arabidopsis Shoot data.

adj.mod <- adj_mod(data=se.fil.arab)

The adjacency matrix is a measure of co-expression similarity between genes, where larger value denotes more similarity.

adj.mod[['adj']][1:3, 1:3]

##           ndhA      petL      psaJ
## ndhA 1.0000000 0.5374043 0.6088355
## petL 0.5374043 1.0000000 0.7779227
## psaJ 0.6088355 0.7779227 1.0000000

The module assignment is a data frame. The first column is ds=2 while the second is ds=3. The numbers in each column are module labels with “0” meaning genes not assigned to any modules.

adj.mod[['mod']][1:3, ]

##      2 3
## ndhA 1 0
## petL 1 0
## psaJ 1 0

The matrix heatmap is implemented in function matrix_hm with 2 modes provided: static or interactive. Figure 9 is the static mode on gene HRE2. Setting static=FALSE launches the interactive mode, where users can zoom in and out by drawing a rectangle and by double clicking the heatmap, respectively.

matrix_hm(geneID="HRE2", data=se.fil.arab, adj.mod=adj.mod, angleCol=80, angleRow=35, cexRow=0.8, cexCol=0.8, margin=c(10, 6), static=TRUE, arg.lis1=list(offsetRow=0.1, offsetCol=0.1))

Figure 9: Matrix Heatmap
Rows are genes and columns are samples. The input gene is tagged by 2 black lines.

In Figure 9, the target gene is displayed in the gene module it belongs to, which is indicated by 2 black lines. The rows and columns are sorted by hierarchical clustering dendrograms. The expression matrix of this module is visualised without being scaled (scale="no"). It can be seen that the expression levels of this module is overall much higher in hypoxia than control, and therefore it could potentially be used to infer the hypoxia response mechanism in Arabidopsis.

5 Network Graphs

The same target gene and module from matrix heatmap can also be displayed as a network. Similarly, the network can be dispayed in static or interactive mode.

Setting static=TRUE launches the static network. In Figure 10 Nodes are genes and edges are adjacencies between genes. The thicker edge denotes higher adjacency (co-expression similarity) while larger node indicates higher gene connectivity (sum of a gene's adjacency with all its direct neighbours). The target gene is labeled by ’_selected’.

network(geneID="HRE2", data=se.fil.arab, adj.mod=adj.mod, adj.min=0.75, vertex.label.cex=1.2, vertex.cex=2, static=TRUE)

Figure 10: Static network
Node size denotes gene connectivity while edge thickness stands for co-expression similarity.

Setting static=FALSE launches the interactive network. There is an interactive color bar to denote gene connectivity. The color ingredients must only be separated by comma, e.g. purple,yellow,blue, which means gene connectivity increases from purple to yellow. If too many edges (e.g.: > 300) are displayed, the network could get stuck. So the ‘Input an adjacency threshold to display the adjacency network.’ option sets a threthold to filter out weak edges. If not too many edges retained (e.g.: < 300), users can check ‘Yes’ under ‘Display or not?’, then the network would be responsive smoothly. To maintain acceptable performance, users are advised to choose a stringent threshold (e.g. 0.9) initially, then decrease the value gradually. The interactive feature allows users to zoom in and out, or drag a gene around. All the gene IDs in the network module are listed in ‘Select by id’ in decreasing order according to gene connectivity. Same with static mode, the target gene ID is appended ’_selected’.

If gene annotation is available in rowData slot and provided to ann argument, the annotation is seen by mousing over a node. In this example, Target.Description in rowData is provided to ann.

network(geneID="HRE2", data=se.fil.arab, ann='Target.Description', adj.mod=adj.mod, static=FALSE)

6 Shiny App

All the above functionality (spatial heatmap, interactive matrix heatmap, interactive network) is also combined into a web-browser based Shiny App, which takes advantage of the computational power of R and interactivity of the web. The main benefits of the Shiny App is combine all the utities in one interface and increase interactivity. On the left of this app is the menu. It includes pre-formatted ready-to-use examples, options to upload formatted data matrix and aSVG images, and instruction to use this app. On the right is the interactive interfacce, including Data Matrix, Spatial Heatmap, Matrix Heatmap, and Network. To use interactive features, there are paramters on the left menu to operate. Upon launched, the app automatically displays a pre-formatted example. A good practice to use this app is to follow steps in the menu rather than skipping steps. If unexpectation happens, the app webpage should be refreshed.

This app is launched by the function shiny_all without any parameters. Figure 11 is the screenshot of Spatial Heatmap.

shiny_all()

Figure 11: The snapshot of Shiny App
Left is the menu and right is the Spatial Heatmap.

The data matrix to upload is a data frame. If the data is a SummarizedExperiment class, the data matrix can be obtained by setting a directory path to dir in function filter_data. A folder local_mode_result/ is automatically created in the provided path, and the filtered data matrix is written to local_mode_result/processed_data.txt with column names in the scheme ’sample__condition’ (Table 1), which is a tab-separated file. If users want to see annotation by mousing over a node in the network, a column of gene annotation in rowData slot should be provided to ann, then the annotation is appended to the last column in processed_data.txt.

For example, in filter_data, setting dir='./' (current working directory) will output the filtered data matrix in ./local_mode_result/processed_data.txt, and setting ann='Target.Description' appends the annotation from rowData slot to the last column of processed_data.txt, which is ready to upload to the app.

se.fil.arab <- filter_data(data=se.aggr.sh, ann="Target.Description", sam.factor='samples', con.factor='conditions', pOA=c(0.03, 6), CV=c(0.30, 100), dir='./')

jianhai_comment: the following Supplement section is substantially changed.

7 Supplement

To plot spatial heatmaps, a pair of data (vector, data frame, SummarizedExperiment) and aSVG image are required. The most important step is to format the data and aSVG image so that target features in aSVG have matching counterparts in the data, since only the matching features in aSVG images are colored. This section explains details of data and aSVG setup that are not covered in the main vignette.

7.1 Format the Data

The accepted data classes include vector, data frame, or SummarizedExperiment (SE). A vector applies to several numeric values measured for a single item (e.g. gene), and data frame applies to more items assayed in several samples and/or several conditions (e.g. 2 samples under 2 conditions). By contrast, SE applies to experiments with many samples and many conditions. Formatting the data is essentially define samples and/or conditions.

Vector
In the case of vector, the numeric values are measured from different samples. If one or more conditions are provided, the samples and conditions should be connected by double undescore, i.e. in the form of ’sample__condition’. If no conditions are provided, all the samples are assumed to have same condition, which is the toy example.

Take 2 samples occipital lobe and parietal lobe from the toy example for instance and assume there are 2 conditions, condition1 and condition2. Select 5 random values, assign 4 of them to the 2 samples under the 2 conditions, and the last one to a not-mapped sample. Note the value names should be unique.

# Random numeric values.
vec <- sample(x=1:100, size=5)
# Give unique names to random values.
names(vec) <- c('occipital lobe__condition1', 'occipital lobe__condition2', 'parietal lobe__condition1', 'parietal lobe__condition2', 'notMapped')
vec

## occipital lobe__condition1 occipital lobe__condition2 
##                         37                         46 
##  parietal lobe__condition1  parietal lobe__condition2 
##                         77                         74 
##                  notMapped 
##                         26

Plot spatial heatmaps.

spatial_hm(svg.path=svg.hum, data=vec, ID='toy', ncol=1, legend.r=1.2, sub.title.size=14)

## Enrties not mapped: notMapped

Figure 12: Spatial heatmaps on a vector
‘occipital lobe’ and ‘parietal lobe’ are 2 aSVG features and ‘condition1’ and ‘condition2’ are conditions.

Data Frame
In the case of data frame, numeric values are measured from different samples. Similarly, if one or more conditions are provided, the column names should be in the form of ’sample__condition’. If no conditions are provided, all the samples are assumed to have same condition.

Take the same samples and conditions in the vector case as example.

Make a numeric data frame of 20 rows and 5 columns. Name columns with the value names (each is unique) from above vector and rows with 20 genes (gene1, gene2, …, gene20).

# Make a numeric data frame.
df.test <- data.frame(matrix(sample(x=1:1000, size=100), nrow=20))
# Name the columns.
colnames(df.test) <- names(vec)
# Name the rows.
rownames(df.test) <- paste0('gene', 1:20)
# A slice of the data frame.
df.test[1:3, ]

## gene2 314 657 ## gene3 365 209 ## parietal lobe__condition1 parietal lobe__condition2 ## gene1 935 181 ## gene2 297 111 ## gene3 877 726 ## notMapped ## gene1 356 ## gene2 776 ## gene3 711

In the downstream interactive network, if users want to have a gene annotation by mousing over a node, a column of gene annotation can be appended to the data frame. For example, the 20 genes are annotated as ann1, ann2, …, ann20.

df.test$ann <- paste0('ann', 1:20)
df.test[1:3, ]

##       occipital lobe__condition1 occipital lobe__condition2
## gene1                        431                        566
## gene2                        314                        657
## gene3                        365                        209
##       parietal lobe__condition1 parietal lobe__condition2
## gene1                       935                       181
## gene2                       297                       111
## gene3                       877                       726
##       notMapped  ann
## gene1       356 ann1
## gene2       776 ann2
## gene3       711 ann3

Plot spatial heatmaps on gene1.

spatial_hm(svg.path=svg.hum, data=df.test, ID=c('gene1'), ncol=1, legend.r=1.2, sub.title.size=14)

SummarizedExperiment

In the following, the same samples and conditions in the above data frame are taken as example.

Formatting data of SummarizedExperiment (SE, Morgan et al. (2018)) is essentially to make a targets file (a data frame of column metadata). The targets file usually has at least 2 columns that specifies sample and condition replicates respectively, and should be added to the colData slot. The data matrix should have assayed items (e.g. genes) and sample/conditions in rows and columns respectively, and must be in the assay slot. The rowData slot can store a data frame of annotaions corresponding to rows in assay slot, but is not required.

To plot spaital heatmap successfully, the targets file should meet the following requirements.

1. It is a data frame and usually has at least one column of samples and one column of conditions. The rows correspond with columns in assay slot. If the condition column is not defined, the samples are assumped under same condition.

2. The sample column specifies sample replicates. It is crucial that replicate names of the same sample must be identical. Otherwise, they are treated as different samples. E.g. occipital lobe, occipital lobe are the same sample while occipital lobe1, occipital lobe2 are different samples.

3. The sample identifiers of interest must be identical with features of interest in aSVG respectively. It means even a dot, undescore, space, etc can make a difference and lead to target features not colored in spatial heatmaps. Since double underscore (__) is a reserved separator in spatialHeatmap, it cannot be used in sample or condition identifiers.

4. The condition column has the same requirement with the sample column. E.g. condition1, condition1 is same conditoin while condition1A, condition1B is treated as different conditions.

In the following example, occipital lobe has 2 conditions condition1 and condition2, and each condition has 2 replicates, so there are 4 assays for occipital lobe. The same applies to parietal lobe. Based on this experiment design, the corresponding targets file is made, where a row is an assay.

# Two samples.
sample <- c(rep('occipital lobe', 4), rep('parietal lobe', 4))
# Two conditions.
condition <- rep(c('condition1', 'condition1', 'condition2', 'condition2'), 2)
# Targets file.
target.test <- data.frame(sample=sample, condition=condition, row.names=paste0('assay', 1:8))
target.test

##                sample  condition
## assay1 occipital lobe condition1
## assay2 occipital lobe condition1
## assay3 occipital lobe condition2
## assay4 occipital lobe condition2
## assay5  parietal lobe condition1
## assay6  parietal lobe condition1
## assay7  parietal lobe condition2
## assay8  parietal lobe condition2

Make a random numeric data frame of 8 columns and 20 rows. Each column is an assay and each row is a gene's expression profile. Columns must correspond with rows in targets file, so column names are assigned assay1-8.

# Make a numeric data frame.
df.se <- data.frame(matrix(sample(x=1:1000, size=160), nrow=20))
# Name the rows.
rownames(df.se) <- paste0('gene', 1:20)
# Replace the default column names. 
colnames(df.se) <- row.names(target.test)
# A slice of the data frame.
df.se[1:3, ]

##       assay1 assay2 assay3 assay4 assay5 assay6 assay7 assay8
## gene1    990    117    516    589    451    464    353    954
## gene2    897    646    619    218    314    279    292    173
## gene3    871    349    839    373    570    550    235    955

se <- SummarizedExperiment(assays=df.se, colData=target.test)
se

## class: SummarizedExperiment 
## dim: 20 8 
## metadata(0):
## assays(1): ''
## rownames(20): gene1 gene2 ... gene19 gene20
## rowData names(0):
## colnames(8): assay1 assay2 ... assay7 assay8
## colData names(2): sample condition

Similarly, in the downstream interactive network, if users want to have a gene annotation by mousing over a node, a data frame of gene annotation can be added to rowData slot, i.e. the ann column in df.test.

rowData(se) <- df.test['ann']

In this simple example, the normalization and filtering process is left out, but replicates should be aggregated. In function aggr_rep, the sample and condition columns in targets file are concatenated with double underscore to form ’sample__condition’ replicates for aggregating.

se.aggr <- aggr_rep(data=se, sam.factor='sample', con.factor='condition', aggr='mean')
assay(se.aggr)[1:3, ]

7.2 aSVG repository

The aSVG repository is from EBI Gene Expression Group, where the requirements on aSVG format are included. It contains aSVGs across different species and can be downloaded with funtion return_feature directly. If users cannot find a target aSVG in this repository, there is a step-by-step SVG tutorial to create custom aSVG images, which is developed by this project.

7.3 Update aSVG features

To change existing feature identifiers in aSVG, the function update_feature should be used. For testing purpose, an empty folder ~/test1 is created and a copy of the aSVG homo_sapiens.brain.svg packaged in spatialHeatmap is saved in there.

# Make an empty directory.
if (!dir.exists('~/test1')) dir.create('~/test1')
# Copy the "homo_sapiens.brain.svg" aSVG.
svg.hum <- system.file("extdata/shinyApp/example", 'homo_sapiens.brain.svg', package="spatialHeatmap")
file.copy(from=svg.hum, to='~/test1', overwrite=FALSE)

Use feature and species keywords to query the aSVG and return existing features, which is a data frame.

feature.df <- return_feature(feature=c('frontal cortex'), species=c('homo sapiens', 'brain'), dir='~/test1', remote=FALSE, keywords.any=FALSE)
feature.df

Make a vector of new feature identifiers corresponding to every returned feature, e.g. replacing spaces with dots. This vector must be added to the first column of the feature data frame, since that is where update_feature looks for new features. Then features are updated with update_feature.

# A vector of new features.
f.new <- c('frontal.cortex', 'prefrontal.cortex')

# New features added to the first column of feature data frame.
feature.df.new <- cbind(featureNew=f.new, feature.df)
feature.df.new

# Update the features.
update_feature(feature=feature.df.new, dir='~/test1')

# Version Informaion
sessionInfo()

## R version 4.0.0 (2020-04-24)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.5 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/libblas/libblas.so.3.6.0
## LAPACK: /usr/lib/lapack/liblapack.so.3.6.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] parallel  stats4    stats     graphics  grDevices utils    
## [7] datasets  methods   base     
## 
## other attached packages:
##  [1] spatialHeatmap_0.99.0       ggplot2_3.3.0              
##  [3] GEOquery_2.56.0             ExpressionAtlas_1.16.0     
##  [5] xml2_1.3.2                  limma_3.44.1               
##  [7] SummarizedExperiment_1.18.1 DelayedArray_0.14.0        
##  [9] matrixStats_0.56.0          Biobase_2.48.0             
## [11] GenomicRanges_1.40.0        GenomeInfoDb_1.24.0        
## [13] IRanges_2.22.1              S4Vectors_0.26.1           
## [15] BiocGenerics_0.34.0         BiocStyle_2.16.0           
## [17] knitr_1.28                  nvimcom_0.9-25             
## 
## loaded via a namespace (and not attached):
##   [1] backports_1.1.7        rols_2.16.1           
##   [3] Hmisc_4.4-0            igraph_1.2.5          
##   [5] lazyeval_0.2.2         shinydashboard_0.7.1  
##   [7] splines_4.0.0          BiocParallel_1.22.0   
##   [9] digest_0.6.25          foreach_1.5.0         
##  [11] htmltools_0.4.0        magick_2.3            
##  [13] GO.db_3.11.1           fansi_0.4.1           
##  [15] gdata_2.18.0           magrittr_1.5          
##  [17] checkmate_2.0.0        memoise_1.1.0         
##  [19] cluster_2.1.0          doParallel_1.0.15     
##  [21] readr_1.3.1            fastcluster_1.1.25    
##  [23] annotate_1.66.0        prettyunits_1.1.1     
##  [25] jpeg_0.1-8.1           colorspace_1.4-1      
##  [27] blob_1.2.1             xfun_0.13             
##  [29] dplyr_0.8.5            crayon_1.3.4          
##  [31] RCurl_1.98-1.2         jsonlite_1.6.1        
##  [33] genefilter_1.70.0      impute_1.62.0         
##  [35] survival_3.1-12        iterators_1.0.12      
##  [37] glue_1.4.1             gtable_0.3.0          
##  [39] zlibbioc_1.34.0        XVector_0.28.0        
##  [41] scales_1.1.1           DBI_1.1.0             
##  [43] edgeR_3.30.0           Rcpp_1.0.4.6          
##  [45] viridisLite_0.3.0      xtable_1.8-4          
##  [47] progress_1.2.2         htmlTable_1.13.3      
##  [49] gridGraphics_0.5-0     flashClust_1.01-2     
##  [51] foreign_0.8-79         bit_1.1-15.2          
##  [53] preprocessCore_1.50.0  Formula_1.2-3         
##  [55] rsvg_2.1               htmlwidgets_1.5.1     
##  [57] httr_1.4.1             gplots_3.0.3          
##  [59] RColorBrewer_1.1-2     acepack_1.4.1         
##  [61] ellipsis_0.3.1         farver_2.0.3          
##  [63] pkgconfig_2.0.3        XML_3.99-0.3          
##  [65] nnet_7.3-14            utf8_1.1.4            
##  [67] locfit_1.5-9.4         dynamicTreeCut_1.63-1 
##  [69] labeling_0.3           ggplotify_0.0.5       
##  [71] tidyselect_1.1.0       rlang_0.4.6           
##  [73] later_1.0.0            AnnotationDbi_1.50.0  
##  [75] visNetwork_2.0.9       munsell_0.5.0         
##  [77] tools_4.0.0            cli_2.0.2             
##  [79] RSQLite_2.2.0          fastmap_1.0.1         
##  [81] evaluate_0.14          stringr_1.4.0         
##  [83] ggdendro_0.1-20        yaml_2.2.1            
##  [85] bit64_0.9-7            caTools_1.18.0        
##  [87] purrr_0.3.4            mime_0.9              
##  [89] compiler_4.0.0         rstudioapi_0.11       
##  [91] curl_4.3               plotly_4.9.2.1        
##  [93] png_0.1-7              tibble_3.0.1          
##  [95] geneplotter_1.66.0     stringi_1.4.6         
##  [97] highr_0.8              lattice_0.20-41       
##  [99] Matrix_1.2-18          vctrs_0.3.0           
## [101] pillar_1.4.4           lifecycle_0.2.0       
## [103] BiocManager_1.30.10    data.table_1.12.8     
## [105] bitops_1.0-6           grImport_0.9-3        
## [107] httpuv_1.5.2           R6_2.4.1              
## [109] latticeExtra_0.6-29    bookdown_0.19         
## [111] promises_1.1.0         KernSmooth_2.23-17    
## [113] gridExtra_2.3          codetools_0.2-16      
## [115] MASS_7.3-51.6          gtools_3.8.2          
## [117] assertthat_0.2.1       DESeq2_1.28.1         
## [119] withr_2.2.0            GenomeInfoDbData_1.2.3
## [121] hms_0.5.3              grid_4.0.0            
## [123] rpart_4.1-15           tidyr_1.0.3           
## [125] rmarkdown_2.1          rvcheck_0.1.8         
## [127] shiny_1.4.0.2          WGCNA_1.69            
## [129] base64enc_0.1-3

8 Funding

This project has been funded by NSF awards: PGRP-1546879, PGRP-1810468, PGRP-1936492.

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